Mn2CoZ „Z=Al,Ga,In,Si,Ge,Sn,Sb… compounds: Structural, electronic, and magneticproperties

G. D. Liu,1 X. F. Dai,2 H. Y. Liu,2 J. L. Chen,1 Y. X. Li,2 Gang Xiao,3 and G. H. Wu1

1Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences,Beijing 100080, People’s Republic of China

2School of Material Sciences and Engineering, Hebei University of Technology, Tianjin 300130, People’s Republic of China3Department of Physics, Brown University, Providence, Rhode Island 02912, USA

�Received 4 April 2007; published 17 January 2008�

We study the electronic structures and magnetic properties of Mn2CoZ �Z=Al,Ga, In,Si,Ge,Sn,Sb� com-pounds with Hg2CuTi-type structure using first-principles full-potential linearized-augmented plane-wave cal-culations. It is found that the compounds with Z=Al, Si, Ge, Sn, and Sb are half-metallic ferrimagnet.Experimentally, we successfully synthesized the Mn2CoZ �Z=Al,Ga, In,Ge,Sn,Sb� compounds. Using thex-ray diffraction method and Rietveld refinement, we confirm that these compounds form Hg2CuTi-typestructure instead of the conventional L21 structure. Based on the analysis on the electronic structures, we findthat there are two mechanisms to induce the minority-spin band gap near the Fermi level, but only the d-d bandgap determines the final width of the band gap. The magnetic interaction is quite complex in these alloys. It isthe hybridization between the Mn�C� and Co atom that dominates the magnitude of magnetic moment of theCo atom and the sign of the Mn�B�-Co exchange interaction. The Mn2CoZ alloys follow the Slater-Pauling ruleMH=NV−24 with varying Z atom. It was further elucidated that the molecular magnetic moment MH increaseswith increasing valence concentration only by decreasing the antiparallel magnetic moment of Mn�C�, whilethe magnetic moments of Mn�B� and Co are unaffected.

DOI: 10.1103/PhysRevB.77.014424 PACS number�s�: 75.50.Cc, 71.20.Lp

I. INTRODUCTION

Half-metallic materials1 exhibiting a complete spin polar-ization �P=100% � at the Fermi surface have received grow-ing interest due to its great value for spintronic devices suchas nonvolatile magnetic random access memories and mag-netic sensors.2 Especially, the half-metallic materials withlow spin magnetic moments seem to be highly desirable forrealistic applications since they lead to smaller energy lossesdue to the lower external magnetic fields created with respectto their ferromagnetic counterparts.3 After the pioneeringwork of von Leuken and de Groot,4 the concept of half-metallic ferrimagnetism and antiferromagnetism receivedconsiderable theoretical interest. Pickett5 and Park et al.6

searched for and investigated the half-metallic antiferromag-netic double-perovskite-structure oxides based on the theo-retical exploration of electronic structures. Akai and Ogurareported the possibility of half-metallic antiferromagnetismin the diluted magnetic semiconductors on the basis of thefirst-principles electronic structure calculation.7

In fact, more investigations on the half-metallic materialswere focused on the Heusler alloy system. It is well knownthat a number of Heusler alloys8 have been predicted basedon first-principles calculations to be half-metallic. Some al-loys, e.g., XMnSb �X=Ni, Co, etc.�,1,9 Co2MnZ �Z=Si,Ga,Ge,Sn�,10–14 and Mn2VZ �Z=Al, Ga, Si, etc.�,15–18

have been investigated experimentally in detail on theirstructural, electronic, and magnetic properties in the past twodecades. Recently, Ozdogan et al. reported the defect-drivenappearance of half-metallic ferrimagnetism in Co-Mn-basedHeusler alloys3 and the defect-induced ferrimagnetism in thehalf-metallic Co2CrAl and Co2CrSi compounds.19 Galanakiset al. investigated the half-metallic antiferromagnetism of the

doped Mn2VAl and Mn2VSi Heusler alloys.20 Increasingevidence has indicated that Heusler-type alloys is a promis-ing set of compounds to search for new half-metallic mate-rials.

Heusler alloys are represented in general by the genericformula X2YZ, where X and Y denote some transition-metalelements and Z an s-p element.21,22 Usually, the ternary com-pounds have a highly ordered L21 structure, which belongsto the Fm3̄m space group. The structure’s prototype is theCu2MnAl alloy. In past studies, the most Mn-contained Heu-sler alloys only have one Mn atom per f.u. with the Mn atomoccupying the Y site in the L21 structure. Few alloys contain-ing two Mn atoms per f.u. were investigated, among whichare the Mn2V-based compounds that are of the L21structure.15–21 However, the Mn2NiSn forms theHg2CuTi-type structure,23 which is different from the con-ventional Heusler alloys. Its space group is F4̄3m, the sameas that of the semi-Heusler alloy.

Recently, we reported that the Mn2NiGa and Mn2CoSballoys prefer to form the Hg2CuTi-type structure.24,25 Thetwo Mn atoms as nearest neighbors to each other bring abouta quite complex magnetic interaction, which lead to a seriesof physical properties for the Mn2Co-based alloys. For ex-ample, Mn2CoSb’s half-metallicity25 is a result of theHg2CuTi-type structure. Mn2CoZ is a potential class of Heu-sler alloys with half-metallicity.

In this work, we present a study on a series of Mn2CoZalloys �Z=Al, Ga, In, Si, Ge, Sn, and Sb�. Most of themexcept Z=Si have been synthesized and structurally charac-terized, as will be described later. We have determined thatthese compounds are of the Hg2CuTi-type structure insteadof the conventional L21 structure. Most interestingly, ourfirst-principles calculations have predicted that the com-

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pounds with Z=Al, Si, Ge, Sn, and Sb are half-metallic ma-terial with ferrimagnetism. We will discuss the formation ofhalf-metallicity and the magnetic properties of these alloys indetail. We will show that there are two mechanisms to inducethe minority-spin band gap near the Fermi level, but only thed-d band gap determines the final width of the band gap. It isthe hybridization between the Mn�C� and Co atom thatdominates the magnitude of magnetic moment of the Coatom and the sign of the Mn�B�-Co exchange interaction. Wewill also show that the Mn2CoZ alloys follow the Slater-Pauling rule MH=NV−24 with varying Z. We will elucidatethat the molecular magnetic moment MH increases with in-creasing valence concentration only by the reduction of theantiparallel magnetic moment of Mn�C�, while the magneticmoments of Mn�B� and Co remain primarily unchanged.

II. EXPERIMENTAL AND COMPUTATIONALDETAILS

Not all the Mn2CoZ alloys with different Z elements canbe synthesized to a pure body-centered cubic �bcc� structureby using the arc-melt method. We have used both the arc-melt and the melt-spun techniques with appropriate anneal-ing process to fabricate Mn2CoZ alloys with pure bcc struc-ture. Initially, we prepared all precursor ingots with relevantcomponents and compositions by arc melting pure metals inthe argon atmosphere. If necessary, some precursor ingotswere melt spun into ribbons with widths of 2–3 mm andthicknesses of 40–50 �m at a linear velocity of 12 m /s;other precursor ingots were encapsulated under argon inquartz glass and annealed at 1073 K for 72 h. Table I listspreparation methods and various parameters for all samplesfabricated. We analyzed the structure of all the samples usingpowder x-ray diffraction �XRD� �Cu K�� and Rietveld re-finement methods. We measured the magnetization of thesesamples using a superconducting quantum interference de-vice magnetometer in fields up to 5 T at 5 K.

Based on the structure and the experimentally determinedlattice constants of the fabricated alloys, we calculated the

electronic structure of the materials using the self-consistentfull-potential linearized-augmented plane-wave �FLAPW�method based on the local density approximation within thedensity functional theory.26,27 Fifty k points in the irreducibleBrillouin zone were used to achieve the self-consistency inthe calculation. The self-consistency is better than0.01 me /a.u. for charge density and spin density and the sta-bility is better than 0.1 mRy for the total energy per cell. Themuffin-tin sphere radii R were chosen as RAl=2.5 a.u., RSi=2.1, RSb=2.6 a.u., RGa=RIn=RGe=RSn=2.3 a.u., and RMn=RCo=2.2 a.u. The density plane-wave cutoff is Rkmax=8.0.The electron states were treated in a scalar relativistic ap-proximation. Using the energy eigenvalues and eigenvectorsat these points, the density of states was determined by thetetrahedral integration method.28,29

III. RESULTS AND DISCUSSIONS

A. Crystal structure

In our previous work, we have reported that Mn2NiGaand Mn2CoSb form the Hg2CuTi-type structure,1,24,25 whosestructural model is shown in Fig. 1. The main differencefrom the conventional Heusler alloys with Cu2MnAl-typestructure is the interexchange between Mn at the C site andCo at B site. XRD examinations for the Cu2MnAl-type orHg2Ti-type structures yield two types of superlattice reflec-tions superposed onto the fundamental diffraction pattern.The diffraction peaks for the �h ,k , l� planes can be catego-rized as follows: a type I superlattice reflection when h, k, lare all odd �e.g., �111� peak�, a type II superlattice reflectionwhen h, k, l are all even and h+k+ l=2n �e.g., �200� peak�,and fundamental reflections where h, k, l are all even andh+k+ l=4n �e.g., �220� peak�.21,30

For materials with these structures, the structure factorsF�111� and F�200� correspond to the order-dependent super-lattice reflections, while F�220� corresponds to order-independent principal reflections. Therefore, the ratio of thesuperlattice intensity to the principal peak intensity providesinformation on the antisite disorder in the following ways:�1� disorder between B and D sublattices reduces the type Isuperlattice peak to zero in the limit of complete disorderand �2� disorder between the A, C, and B superlattices re-duces the intensities of type II superlattice peaks relative tothat of the principal reflections.30

TABLE I. The fabrication method, lattice constant, calculatedband gap, and spin-flip gap �HM gap� for Mn2CoZ �Z=Al, Ga, In,Si, Ge, Sn, Sb� compounds. The symbol “ �” indicates that thelattice constant is hypothetic and the other was obtained by experi-mental results.

CompostionMn2CoZ

Fabricationmethod

Latticeconstant

��

Bandgap�eV�

HMgap�eV�

Al Arc melt 5.8388 0.2245 0.016

Ga Arc melt 5.8620 0.05 −0.100

In Arc melt 6.1420

Si 5.8000* 0.3971 0.188

Ge Annealing 5.8000 0.2692 0.100

Sn Melt spun 6.0588 0.09410 0.070

Sb Melt spun 5.9042 0.4004 0.134

Sn 5.8000* 0.2291 0.050

(a) (b) (c)

FIG. 1. �a� The generalized Heusler structure with four interpen-etrating fcc sublattices A, B, C, and D. The structure models ofMn2CoZ: �b� the Hg2CuTi-type structure and �c� the conventionalL21 structure.

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The experimental XRD patterns for powdered Mn2CoZ�Z=Al,Ga, In,Ge,Sn,Sb� are shown in Fig. 2. For theMn2CoZ �Z=Al,Ga,Ge,Sn,Sb� alloys, all the principal re-flection peaks of bcc structure are observed without the othersecondary peaks on the XRD patterns, indicating that theMn2CoZ form the pure bcc structure. Furthermore, it is notedthat all the XRD patterns for Mn2CoZ alloys with bcc struc-ture display the �111� and �200� peaks, which strongly sug-gests that a highly ordered Hg2CuTi-type structure has beenformed in these alloys. The Rietveld refinement analyseswere carried out to identify the degree of atomic ordering inthese alloys. Using the Hg2CuTi-type model, the Rietveldrefinement results are also shown in Fig. 2. It is clear that theobserved XRD patterns match the refinement results verywell. We also used the Cu2MnAl-type model to refine theexperimental data and the results show a worse fit than thatusing the Hg2CuTi-type model, which is similar to the casein Mn2NiGa and Mn2NiSn.23,24

In the Mn2CoIn alloy, there is a small amount of secondphase �� phase with fcc structure� embedded in the main bccstructure, as seen in the XRD pattern of Fig. 2�c�. The �111�and �200� superlattice peaks can still be observed in the XRDpattern of the Mn2CoIn alloys though the experimental inten-sity of the �111� peak is slightly weaker than the calculatedvalue. As mentioned earlier, the weakness of the �111� peak

can be attributed to the small antisite disordering betweenMn�C� and In. For Z=Si, we were not able to form the bccstructure using whatever method.

Burch et al. showed that in the Fe3Si compound �theFe3Si can be considered as Fe2FeSi with a Heusler structure�,partly substituting transition metals �as impurities� for Fereveals a noticeable preference of occupation of one type ofFe site depending on the number of 3d electrons. Transition-metal impurities on the left-hand side of Fe in the PeriodicTable �e.g., Mn or V� demonstrate strong preference for Bsite occupation, whereas atoms on the right side of Fe �e.g.,Co� prefer �A ,C� sites.31,32

For the Mn2YZ compounds, we also observed a rule simi-lar to that reported by Burch et al. We have observed that ifY elements are Ni or Co �on the right-hand side of Mn�, theyprefer to occupy the �A ,C� sites in Mn2Ni- andMn2Co-based compounds and be crystallized in theHg2CuTi-type structure. When the Y atom is V �on the left-hand side element of Mn�, it shows a strong preference for Bsite occupation in Mn2V-based alloys and is crystallized inconventional Cu2MnAl-type structure.11–14 Based on thisrule, it is easy to estimate the superlattice structure of theHeusler-like compounds. Furthermore, we can also considerthe rule to be fit to the quaternary alloys. In addition, theselectivity of occupation for our materials is also supportedby the first-principles total energy calculations, which will bereported elsewhere. So, we believe that our Mn2CoZ alloysformed the Hg2CuTi-type structure.

B. General discussion on electronic structure

The lattice parameters of Mn2CoZ obtained experimen-tally were shown in Table I. One exception is the latticeparameter for Mn2CoSi, which we assumed to be 5.80 Å, thesame as that of Mn2CoGe, as we have not experimentallysynthesized the alloy. The Hg2TiCu-type model with idealoccupation of elements was used to carry out the first-principles calculation. In addition, to separate the influenceof the lattice constant and the binding energy of p electrons,we also show the related data in Table I for the Mn2CoSncompound with the lattice of 5.80 Å, which is smaller thanthe experimental result but equal to that of Mn2CoZ �Z=Si,Ge�.

Figures 3–5 display the band structures of Mn2CoZ com-pounds with Hg2TiCu-type structure for the spin-up �major-ity� and the spin-down �minority� electrons. It is evident thatthe majority band structure has metallic intersections for allcompounds at the Fermi level, indicating a strong metallicnature of the majority electrons. However, the minority bandstructure of these alloys exhibits a band gap near the Fermilevel except for Mn2CoIn. Therefore, our calculation revealsthat Mn2CoZ �Z=Al, Si, Ge, Sn, and Sb� alloys may formanother family of half-metals. For the alloys with Z=Ga, theminority valence band maximum is only slightly above theFermi level, yielding a rather small density of states at theFermi level. For the alloys with Z=In, the Fermi level fallsinto a deep valley and there are a little density of states at theFermi level. Alloys with Z=Ga and In may exhibit weakenedhalf-metallic properties.

20 30 40 50 60 70 80 90

(f)

2� (degree)

(422)

(420)

(331)

(400)

(222)

(311)(220)

(200)

(111)

Mn2CoSb

(e)

(420)

(331)

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(422)

(400)(220)

(200)

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(311)

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(200)

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Mn2CoGe

(c)

RelativeIntensity(a.u.)

� phase� phase

(420)

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(222)

(311)

(422)

(400)

(220)

(200)

(111)

Mn2CoIn

(b)

(420)

(331)

(222)

(311)

(422)

(400)(220)

(200)

(111)

Mn2CoGa

(a)

(420)

(331)

(222)

(311)

(422)

(400)(220)

(200)

(111)

Mn2CoAl

FIG. 2. X-ray diffraction patterns of Mn2CoZ �Z=Al,Ga, In,Ge,Sn,Sb� alloys: experimental data ��� for the pow-der samples and calculated data �continuous line� for theHg2CuTi-type model. The bottom curve shows the difference be-tween experimental and calculated data on the same scale as thediffraction.

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FIG. 3. Majority-spin �left column� and minority-spin �right column� band structures for Mn2CoZ �Z=Al,Ga, In� alloys at the experi-mental lattice constants of 5.8388, 5.8620, and 6.1420 Å, respectively.

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With the help of the density of states �DOS�, as shown inFigs. 6–12, it is clear that the energy regions of −7 to−10 eV �for Z=Al, Ga, In�, −9.5 to −12 eV �for Si, Ge, Sn�,and −10.5 to −13.5 eV �for Sb� consist mainly of s electrons

of the Z atoms �4s or 5s� and the band structure is almostidentical for both spin directions. These lowest valencebands are separated from the other valence bands by an en-ergy gap for both majority and minority spins and unaffected

FIG. 4. Majority-spin �left column� and minority-spin �right column� band structures for Mn2CoSi at the hypothetic lattice constant of5.80 Å and Mn2CoZ �Z=Ge,Sn� alloys at the experimental lattice constants of 5.80 and 6.042 Å, respectively.

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by the Co-Mn or Mn-Mn exchange interaction. Therefore,the s electrons have little influence on the magnetic momentand the formation of a half-metallic band gap, except extend-ing the valence to a broader range. We did not show these sbands in the band graphs of Fig. 3–5. The energy regionbetween −7 and 0 eV consists mainly of the d electrons ofCo and Mn atoms. These dispersed bands are due to thestrong hybridization of Mn-Mn and Mn-Co d electrons, in-cluding a contribution from Z p states in the occupied va-lence states.

From the total DOS, as shown in Figs. 6–12, one can seethat the shape of all the density of states is similar except forsome detailed difference. For the majority-spin states, thereappear to be three peaks. The two peaks at the lower energiescan be traced to the eg− t2g splitting in the cubic crystal field,and the peak at the higher energy is composed of antibondingd bands of mostly Mn�C� character. For the minority-spinstates, two main peaks can be observed. The peak at about1.3 eV above Fermi level is of an antibonding nature mainlyarising from the Mn�B� atom.

The covalent hybridization between the lower-energy dstates of the high-valent transition-metal atom such as Ni orCo and the higher-energy d states of the lower-valent transi-tion metal can lead to the formation of bonding and anti-bonding bands. The bonding hybrids are localized mainly atthe high-valent transition-metal atom site, while the unoccu-pied antibonding states are localized mainly at the lower-valent transition-metal site.4 In order to reveal the situationmore clearly, we also show the partial DOS �PDOS� for the dcomponent for Co, Mn�B�, and Mn�C� atoms and s, p com-ponents for the Z atoms in Figs. 6–12. It is clear that thereare strong hybridizations between the transition-metal atoms.The bonding states are mainly localized at the Co site, whilethe antibonding states are localized at the Mn�B� site formajority-spin states and at the Mn�C� site for minority-spinstates.

In addition, the p electrons of the s-p element also hybrid-ize with the d states, which determine the degree of occupa-tion of the p-d orbitals. We should note that the energy of thep electrons is strongly dependent on Z atoms, which can beclearly seen in the PDOS patterns. The hybridization be-tween p electrons with different energies and d electrons iscrucial to the width of the energy gap in the minority-spinband, as will be illustrated below.

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(a) Ef

Energy (eV)

DOS(States/eVatomspin)

Total

(d) Co-d

(c) Mn(B)-d

(b) Mn(C)-d

(e) Al-sAl-p

FIG. 6. Calculated spin-projected DOS plots for Mn2CoAl at theexperimental lattice constant of 5.8388 Å. �a� The total DOS ofMn2CoAl, �b� the partial DOS of the d component of Mn�C� atoms,�c� the partial DOS of the d component of Mn�B� atoms, �d� thepartial DOS of the d component of Co atoms, and �e� the partialDOS of s and p components of Al atoms. The upper halves of eachpanel display the spin-up states and the lower halves the spin-downstates.

FIG. 5. Majority-spin �left column� and minority-spin �right column� band structures for Mn2CoSb alloy at the experimental latticeconstant of 5.8620 Å.

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C. Origin of the band gap

In this section, we will focus on the energy gap inminority-spin states. Such a gap is the most important featureof a half-metal. In the alloys with composition of Z=Al, Ga,Si, Ge, Sn, and Sb, the calculated results show an indirect�-X band gap for the minority carriers, as shown in Figs.3–5. The detailed data are listed in Table I. The origin of theband gap is usually distinguished into three categories: �1�covalent band gap, �2� d-d band gap, and �3� charge transferband gap.33 The covalent band gap has been shown to existin semi-Heusler alloys with C1b structure �e.g., NiMnSb�.The d-d band gap is responsible for the half-metallicity ofthe full-Heusler alloys with L21 structure �e.g., Mn2VAl�.The charge transfer band gap is usually common in CrO2 anddouble perovskites.

In our Mn2CoZ alloys, the situation is more complex dueto the special crystallized structure �as shown in Sec. III A�.The Mn2CoZ alloys have a space group similar to the semi-Heusler CoMnZ alloys but the empty site was alternated bythe additional Mn atom. Compared with the full-Heusler al-loy with L21 structure �Mn2VAl�, the Mn atoms occupy twosublattices with different surroundings in Mn2CoZ alloys.Therefore, we must pay attention to the effects of these twoMn atoms.

To understand the origin of the band gap, let us observeagain the PDOS shown in Figs. 6–12. First, we focus on theMn�B� atom. It can be seen that all of the Mn�B� atoms in

the Mn2CoZ alloys have the similar feature of DOS. Theminority-spin band structure can be characterized by thelarge band gap near the Fermi level and the unoccupied an-tibonding bands at higher energies. Mn�C� and Co atoms arethe nearest neighbors of Mn�B�. As mentioned in Sec. III B,there is a strong covalent hybridization between the d statesof Mn�C�, Co, and Mn�B�, which leads to the formation ofthe bonding and antibonding bands separated by the gap.Therefore, the gap in the minority-spin states of Mn�B�arises primarily from the covalent hybridization similar tosemi-Heusler half-metal alloys �e.g., NiMnSb andCoMnSb�.9

For Mn�C� and Co atoms, the situation is very differentfrom the Mn�B� atom. They have a similar gap width, whilethe Mn�B� atom has a larger gap width. Hence, the actualgap width in the Mn2CoZ compounds is determined mainlyby the Mn�C� and Co atoms. Furthermore, it can be under-stood that it is the tail of the d states of the Mn�C� and Cohybridized with Z p states that determines the character ofthe minority-spin gap. Obviously, the highest occupied mi-nority states mainly consist of d states of Mn�C� and Coatoms. Also, there is a peak at about 0.5 eV above the Fermilevel in the minority-spin states of the Mn�C� and Co atoms,which is lower than the antibonding peak of Mn�B� and onlyhas a small overlap with the antibonding states of Mn�B� inenergy, indicating that a hybridization only occurs betweenMn�C� and Co. Therefore, it may be reasonable to considerfirst the interactions between the Mn�C� atom and the Coatom and then the interaction with the Mn�B� or the s-p

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(e) Ga-pGa-sD

OS(States/eVatomspin)

Energy(eV)

(d) Co-d

(c) Mn(C)-d

(b) Mn(B)-d

(a) Ef Total

FIG. 7. Calculated spin-projected DOS plots for cubicMn2CoGa at the lattice constant of 5.8620 Å. �a� The total DOS ofMn2CoGa, �b� the partial DOS of the d component of Mn�C� atoms,�c� the partial DOS of the d component of Mn�B� atoms, �d� thepartial DOS of the d component of Co atoms, and �e� the partialDOS of s and p components of Ga atoms. The upper halves of eachpanel display the spin-up states and the lower halves the spin-downstates.

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(e) In-sIn-p

(d) Co-d

(c) Mn(C)-d

(b) Mn(B)-d

Ef

Energy(eV)

DOS(States/eVatomspin)

(a) Total

FIG. 8. Calculated spin-projected DOS plots for Mn2CoIn withthe experimental lattice constant of 6.140 Å. �a� The total DOS ofMn2CoIn, �b� the partial DOS of the d component of Mn�B� atoms,�c� the partial DOS of the d component of Mn�C� atoms, �d� thepartial DOS of the d component of Co atoms, and �e� the partialDOS of s and p components of In atoms. The upper halves of eachpanel display the spin-up states and the lower halves the spin-downstates.

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atom, as was also the case for the Co2MnZ �Ref. 34� andFe2MnZ.35

The Heusler alloy has a tetrahedral Td symmetry. How-ever, if we neglect the B and D sites, the lattice consisting ofonly A and C sites has the Oh symmetry. Td is a subgroup ofOh. Thus, it is possible to have states located only at the Aand C sites as there are no states at the B site with the samerepresentation. Based on these, Galanakis et al. successfullyexplained the origin of the band gap of Co2MnZ alloys. Thesituation in our Mn2CoZ alloys is quite similar to that inCo2MnZ. The possible hybridization between spin-down or-bitals sitting at the different sites in the case of our Mn2CoZalloys will create several energy levels: eg, t2g, eu, and t1u.The exchange splitting will shift the Fermi level to the ap-propriate position. As elucidated above, the states at twoedges of the band gap is mainly of Mn�C� and Co charactersinstead of Mn�B� ones. So, as in the Co2MnZ alloy, the statescan be well ascribed to the doubly degenerated eu state andtriply degenerated t1u state, which only arise from the hybrid-ization with Mn�C� and Co d states.34 The eu and t1u orbitalscannot couple with any of the Mn�B� d orbitals as theMn�B� d orbitals do not transform with the u representations.Furthermore, we point out that the t1u states are below theFermi level, while the eu states are just above the Fermi leveldue to the fact that the total eight minority d bands are filledin our Mn2CoZ compounds. So, it is clear that the band gapof the Mn�C� and Co atom is the d-d band gap, and it arisesonly from the eu− t1u splitting instead of the conventionaleg− t2g one in Heusler alloys.

The Mn�C� and Co atoms are the second nearest neigh-bors; therefore, the eu− t1u splitting is weak and leads to a

smaller gap than that of the Mn�B� atom. In conclusion, itshould be emphasized that there exist two mechanisms in theformation of the band gap in the Mn2CoZ compounds, thatis, covalent band gap and d-d band gap, but it is mainly thed-d band gap that characterizes the half-metallicity inMn2CoZ alloys.

From Table I, we can also find that the width of the en-ergy gap decreases with increasing atomic number in a groupof the Periodic Table �e.g., Si→Ge→Sn� but increases in arow �e.g., In→Sn→Sb�, which is also observed in the full-Heusler alloy Co2MnZ �Z=Si,Ge,Sn�.14 As elucidated inRef. 10, the change of the width of the gap can be tracedback to two combined effects: �1� p-d hybridization, whichobviously depends on the Z p states, and �2� their differentlattice constants. From the PDOS of p states of the Z atom,as shown in Figs. 6–12, it is clear that the binding energy ofp states of Z atoms decreases with increasing atomic numberin a group and increases in a row, which seems quite well toillustrate the change of the gap as stated above. In fact, theeffect of p-d hybridizations covers up the effect of latticeconstant as the contraction or expansion of the lattice mainlyhas an influence on the delocalized p electrons but not to thealready well localized d electrons of the transition metal. Inorder to further expound the influence of the lattice and thebinding energy of p electrons, we also show the related datain Table I for the Mn2CoSn compound with the lattice pa-rameter of 5.80 Å, which is smaller than the experimentalresult. Clearly, it can be seen that the contraction of the lat-tice enlarges the energy gap. Compared with the Mn2CoSiand Mn2CoGe compounds with the equivalent lattice con-stant, it is also confirmed that the decreasing binding energysqueezes the energy gap.

-8 -6 -4 -2 0 2 4-1.2-0.60.00.61.2-202-202-4-2024-4048

Energy (eV)

DOS(States/eVatomspin)

(e) Si-sSi-p

(d) Co-d

(c) Mn(C)-d

(b) Mn(B)-d

Ef(a) Total

FIG. 9. Calculated spin-projected DOS plots for Mn2CoSi withthe hypothetic lattice constant of 5.800 Å. �a� The total DOS ofMn2CoSi, �b� the partial DOS of the d component of Mn�B� atoms,�c� the partial DOS of the d component of Mn�C� atoms, �d� thepartial DOS of the d component of Co atoms, and �e� the partialDOS of s and p components of Si atoms. The upper halves of eachpanel display the spin-up states and the lower halves the spin-downstates.

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-101

-202-202-4-202-6-3036

(e) Ge-sGe-p

(d) Co-d

(c) Mn(C)-d

Energy (eV)

DOS(States/eVatomspin) (b) Mn(B)-d

(a) Total

FIG. 10. Calculated spin-projected DOS plots for Mn2CoGewith the experimental lattice constant of 5.80 Å. �a� The total DOSof Mn2CoGe, �b� the partial DOS of the d component of Mn�B�atoms, �c� the partial DOS of the d component of Mn�C� atoms, �d�the partial DOS of the d component of Ni atoms, and �e� the partialDOS of s and p components of Ge atoms. The upper halves of eachpanel display the spin-up states and the lower halves the spin-downstates.

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The spin-flip gaps �HM gap�, the minimum energy re-quired to flip a minority-spin electron from the valence bandmaximum edge to the majority-spin Fermi level, are the mostproper indication of the half-metallicity of material. The de-tailed data have also been shown in Table I. It is clear thatthe HM gap shows a change with the atomic number similarto that of the band gap. However, a distinction can be ob-served by the comparison between the Mn2CoSn with differ-ent lattice constants, that is, the contraction of the latticedecreases the HM gap, which is also observed in Co2MnZalloys and can be ascribed to the different Fermi level posi-tions pinned in the band gap due to the rigid band shift withthe change of lattice constant.

D. Magnetic properties and Slater-Pauling rule

The preceding discussion is concerned with the bandstructure and the formation of the band gap. We now turn tothe magnetic properties. The calculated and experimentalmagnetic moments for the compounds and for the single con-stituents are reported in Table II. The Mn�B� atom carries thelargest moment �around 3 �B� in all the Mn2CoZ compounds,which is similar to most of the Mn-based Heusler alloys. TheCo atom has a positive moment of about 1 �B, which issimilar to that in the full-Heusler Co2MnZ alloys but differ-ent from that in semi-Heusler CoMnZ alloys. �At least, it is

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0

4-4

0

4-404

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(e) Sn-sSn-p

(d) Co-d

(c) Mn(C)-d

(b) Mn(B)-d

Energy (eV)

DOS(States/eVatomspin) Ef(a) Total

FIG. 11. Calculated spin-projected DOS plots for cubicMn2CoSn with the experimental lattice constant of 6.0688 Å. �a�The total DOS of Mn2CoSn, �b� the partial DOS of the d compo-nent of Mn�B� atoms, �c� the partial DOS of the d component ofMn�C� atoms, �d� the partial DOS of the d component of Ni atoms,and �e� the partial DOS of s and p components of Sn atoms. Theupper halves of each panel display the spin-up states and the lowerhalves the spin-down states.

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-2

0

2

-4

-2

0

2

4-4

-2

0

2-8

-4

0

4

8

(e) Sb-sSb-p

DOS(States/eVatomspin)

Energy (eV)

(d) Co-d

(c) Mn(B)-d

(b) Mn(C)-d

(a) Ef Total

FIG. 12. Calculated spin-projected DOS plots for cubicMn2CoSb at the lattice constant of 5.8806 Å. �a� The total DOS ofMn2CoSb, �b� the partial DOS of the d component of Mn�C� atoms,�c� the partial DOS of the d component of Mn�B� atoms, �d� thepartial DOS of the d component of Co atoms, and �e� the partialDOS of s and p components of Sb atoms. The upper halves of eachpanel display the spin-up states and the lower halves the spin-downstates.

TABLE II. The magnetic moment on atoms, calculated molecular magnetic moment MC, and the experi-mental molecular magnetic moment ME.

CompositionMn2CoZ

Mn�B���B�

Mn�C���B�

Co��B�

Z��B�

MC

��B�ME

��B�

Al 3.08 −1.98 0.92 −0.02 2.00 1.95

Ga 3.26 −2.16 0.90 0.00 2.00 1.98

In 3.54 −2.60 1.00 0.02 1.95 1.90

Si 3.12 −0.96 0.82 0.02 2.99

Ge 3.14 −0.98 0.82 0.02 2.99 2.99

Sn 3.48 −1.54 0.94 0.04 2.99 2.98

Sb 3.20 −0.04 0.84 0.02 3.99 3.92

Mn2CoZ �Z=Al,Ga, In,Si,Ge,Sn,Sb� COMPOUNDS: … PHYSICAL REVIEW B 77, 014424 �2008�

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well known that the magnetic moment of Co is antiferromag-netically aligned with respect to the Mn atom in semi-Heusler CoMnSb.9� We should pay more attention to theMn�C� atom as it shows the most notable difference from thefull-Heusler alloys with L21 structure and semi-Heusler al-loys. The Mn�C� atom exhibits a varying magnetic momentwith the different s-p atoms in the Mn2CoZ alloys andcouples antiferromagnetically to the Mn�B� and Co mo-ments. Therefore, the total moments are 2 �B, 3 �B, and 4 �Bin the compounds with s-p elements of groups III, IV, and V,respectively, which are in good agreement with experimentalvalues. It should also be pointed out that the integer value ofthe total magnetic moment is an indication of the half-metallic character.

It is known that in Heusler alloys, the ferromagnetic andantiferromagnetic moment alignments result from a compe-tition between two physical mechanisms: the intra-atomicexchange splitting of the magnetic atom d states and theinteratomic covalent interaction of d states.36 The magneticenergy applies equally to the ferromagnetic and antiferro-magnetic alignments, while the covalency mechanism ben-efits only the antiferromagnetic alignment. However, an in-trinsic aspect of the covalency mechanism is a loss of localmagnetization, which is the essence of the antiferromagnetic-ferromagnetic competition.10,36

As shown in our previous report on the Mn2NiGa withHg2CuTi structure, the Mn�C� atom is one of the nearestneighbors of the Mn�B� atom and has a small distance be-tween them. So, we consider that there exists a strong directinteraction between their d states. Hence, the covalencymechanism is dominant to form the antiferromagnetic align-ment between the Mn�C� moment and the Mn�B� moment.In order to further elucidate the character and action ofMn�C� in Mn2CoZ compounds, as a typical example, wehave compared Mn2CoSb with Hg2CuTi structure with semi-Heusler CoMnSb.9,13,38 In the case of the half-Heusler alloys,there is only one Co atom per unit cell and its d valenceelectrons hybridize with the Mn d valence electrons, creatingan antiferromagnetic alignment. In the Mn2CoZ alloys, theexistence of the second Mn atom makes the physics of thesesystems more complex. The Mn�C� atom has a stronger hy-bridization with the Co atom than with the Mn�B� atom,which can be clearly observed from the PDOS shown inFigs. 6–12. So, as the second Mn is added, the reconstructionof the bands is mainly driven by hybridization between theMn�C� d states and Co ones.

In the PDOS of Co d and Mn�C� d states, we can obvi-ously observe a peak at about 0.5 eV above Fermi level forthe minority-spin states in Mn2CoZ alloys, which is not ob-served in the CoMnSb compound. So, this peak is com-pletely induced by the Mn�C� atom. The occurrence of thispeak decreases the minority-spin states of the Co atom belowthe Fermi level. As a consequence, the Co moment shows apositive moment of about 1 �B. It should also be noted thatthe Mn�C� atom has only a small magnetic moment in theMn2CoSb alloy. So, it is impossible that a strong exchangeinteraction between the Mn�C� and Co or Mn�B� atoms ex-ists. Therefore, it can be concluded that the hybridizationbetween the Mn�C� and Co atoms not only changed the mag-

nitude of magnetic moment of the Co atom but also domi-nated the sign of the Mn�B�-Co exchange interaction. Fur-thermore, associated with the compounds with largemagnetic moment of Mn�C�, we can believe that theMn�B�-Co and Mn�B�-Mn�C� exchange interactions are theleading ones in Mn2CoZ alloys, but the hybridization be-tween the Mn�C� and Co atoms dominates the sign of theMn�B�-Co exchange interaction. Usually, we think that thelarger the magnetic moment, the stronger the exchange inter-action. So, it is considered that the stronger Mn�B�-Co andMn�B�-Mn�C� exchange interaction and the higher Curietemperature exist in the compounds with larger magneticmoment of Mn�C�. The related work is being carried out. Inaddition, here, we must emphasize that the Mn�C� and Coare not nearest neighbors and their d electron energy isclosely related to the p electron energy of the Z atom. So, weconsider that the hybridization action of p electrons is nec-essary, although the Mn�C� and Co d states play the pivotalrole to reconstruct the band structure change, the formation,and the coupling of magnetic moments.

As is well known, the half-metal Heusler alloys follow theSlater-Pauling rule. Many researchers focus on the alterna-tive of the transition metal. Here, we want to investigate thebehavior when we vary the valence of the s-p atom in theMn2CoZ alloy system with the special crystallized Hg2CuTistructure. Half-metallic ferromagnets exhibit a gap in the mi-nority density of states where the Fermi energy is pinned,which leads to the number of occupied minority states beingan integer. Thus, the Slater-Pauling rule will be strictly ful-filled with mHMF=nV−6 �nV is the mean number of valenceelectrons per atom� for the spin magnetic moment per atom.In the case of four atoms per unit cell, as in full-Heuslercompounds, one has to subtract 24 from the accumulatednumber of valence electrons NV to find the spin magneticmoment M per unit cell: MH=NV−24.37

From Table II, one can clearly see that, as full-Heusleralloys with L21 structure, the Mn2CoZ alloys also follow theMH=NV−24 rule with varying Z atom. Furthermore, it wasfound that the spin magnetic moment M per unit cell in-creases with increasing valence concentration only by de-creasing the magnetic moment of the antiparallel Mn�C�atom, while the magnetic moments of Mn�B� and Co arebarely touched. Our interpretation is that the changes of the pelectron number only have a strong influence on the mag-netic moment of the Mn�C� atom. The reason is that the s-patom that provides p electrons for the p-d hybridization isone of the nearest neighbors of Mn�C� and the Mn�C� atomhas more empty bands in the majority-spin states, whichmakes it easier to seize electrons than the Co atom. So, fromthe PDOS of Mn�C� d states, as shown in Figs. 6–12, onecan clearly see that the occupation degree of majority-spinbands of Mn�C� increases with increasing group number ofs-p atom �e.g., along In→Sn→Sb� in the Periodic Table andthe negative magnetic moment of Mn�C� becomes smallerand smaller. At the same time, we can also see that the en-ergy of p electrons decreases and departs away from theenergy where the d electron is mainly localized with increas-ing group number of s-p atom. This leads to the weakness ofthe s-p atom-mediated covalent interactions between Mn�C�

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and Co, and the intra-atomic exchange interactions arepopped out, that is, there are more bands in the majority-spinstates of Mn�C� that are shifted and go below the Fermilevel. Thus, although there are more occupied bands in themajority-spin states of Mn�C�, the Fermi level is shiftedslightly and remains to be pinned in the band gap ofminority-spin states, which implies that the change of thenumber of p electrons does not destroy the half-metallicity.

IV. CONCLUSION

Using the FLAPW method, we have studied the Mn2CoZcompounds with Hg2CuTi-type structure. It is predicted thatthe compounds with Z=Al, Si, Ge, Sn, and Sb are half-metals. We find that there exist two mechanisms to inducethe band gap �covalent band gap and d-d band gap� near theFermi level in the minority-spin states. Only the d-d bandgap determines the final width of the band gap, which isdifferent in the two-Mn-contained compounds with conven-tional L21 structure and semi-Heusler alloys, where there isonly one mechanism at work. The magnetic moment ofMn�C� is antiferromagnetically aligned to that of Mn�B� andCo. It is considered that the hybridization between theMn�C� and Co atoms dominates the magnitude of magneticmoment of the Co atom and the sign of the Mn�B�-Co ex-

change interaction. As in conventional full-Heusler alloy, theMn2CoZ alloys follow the Slater-Pauling rule MH=NV−24with varying Z atom. However, the molecular magnetic mo-ment MH increases with increasing valence concentrationonly by decreasing the magnetic moment of the antiparallelMn�C� atom, while the magnetic moments of Mn�B� and Coare untouched and the Fermi level is shifted slightly andremains to be pinned in the band gap of minority-spin states.Therefore, we predict that partly substituting one kind of s-pelement for another will improve the other properties of thematerial but not destroy their half-metallicity. Experimen-tally, we successfully synthesized the Mn2CoZ �Z=Al,Ga, In,Ge,Sn,Sb� compounds and confirmed that thesecompounds favor to form Hg2CuTi-type structure instead ofconventional L21 structure. In this structure, the two Mn at-oms are nearest neighbors to each other and exhibit differentmagnetic characters. Therefore, we believe that it is the spe-cial crystallized structure that leads to a quite complex mag-netic interaction and bring about many physical propertiesfor the Mn2Co-based alloys.

ACKNOWLEDGMENTS

This work was supported by the National Natural ScienceFoundation of China Grant No. 50671034 and the NaturalScience Foundation of Hebei Grant No. E2006000063.

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